Energy-bounded flow approximation on a Cartesian-product grid over rough terrain (Q1261354)

We construct a method for modelling of three-dimensional, time dependent, compressible fluid flow in a gravitational field on a rotating Cartesian- product grid with a spatially rough metric that bounds solutions by the total initial physical energy. Specifically: (1) the total physical energy is an \(l_ 2\) norm on the model state and (2) this total energy cannot increase provided the timestep does not exceed CFL limits. Energy- bounded approximations of fluid flow are then constructed either from antisymmetric finite difference operators, or from antisymmetric Galerkin operators. We demonstrate the method for an ``internal hydraulic jump'' flow over a bell-shaped mountain, simulating an internal wave as it steepens and breaks to form a turbulent jump.